HbA1c of 51 is not at all drastic, and with a suitable diet you will be able to get this right down by the time of your next test.
My advice is ignore your nurse. She is spouting the NHS advice about eating carbs with every meal and low fat. It is known as the Eatwell Plate, which is most likely fine for non-diabetics, but absolutely not fine for type 2s. . It isn't her fault, it is how she was trained. If she is a non-medicated type 2 then I bet either she doesn't follow her own advice or her HbA1c is double yours.
My nurse told me to eat jacket potatoes with baked beans for lunch.
The majority of us, when diagnosed, were told the same as you. I tried the reduced sugar baked beans. They were just as bad as the normal ones.
Your meter will tell you who is right. Test before you eat and again 2 hours after first bite. Your levels should not be any more than 2mmol/l higher, preferably a lot less. Initially, many people also test at 1 hour, then 90 minutes, then 2hrs and if still high keep going to see how long it takes to get back to where you started. This is a good way to learn which foods are really bad for you personally. (recording your levels alongside a food diary).
Your cholesterol of 5 is perfect by the way, although on its own it means very little. You need to know the breakdown of HDL/LDL/Triglycerides and the total/HDL ratio. If you don't know these, ask for a print out of all your results. You will find these invaluable in time to come, and before you decide to take statins.
Some people find saturated fats don't help their cholesterol, but many of us are fine. It is normally carbs that cause the problems, not fats. My cholesterol went right down after I started LCHF and after over 2 and a half years continues to be good.